A Novel Access Control and Energy-Saving Resource Allocation Scheme for D2D Communication in 5G Networks

College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China Department of Mathematics and Information Engineering, Dongchang College of Liaocheng University, Liaocheng 252000, China Shandong Institute of Space Electronic Technology, Yantai 264000, China Department of Computer Science and Engineering, Korea University, Seoul 02841, Republic of Korea

users and multiple D2D links could reuse all cellular users' resources at the same time. It decomposed the original nonconvex optimization problem into two subproblems, and iterative algorithm was used to solve the problem, but it did not consider access control of D2D links. e method of graph theory was introduced into D2D resource allocation [9], which took cellular link, D2D link, and spectrum channel as vertices in the graph. e superedge in the graph corresponded to each channel allocation scheme. Based on this, the cyclic iteration algorithm and branch and bound method were designed to optimize the maximum weight rate of the system. However, in this scheme, each cellular user and each D2D user could occupy one channel at most, thus limiting the spectrum utilization. Yang et al. [10] studied the resource allocation and power control of D2D and cellular users in a single cellular D2D network. Multiple pairs of D2D users could share the same resources with cellular users, the goal of which was to maximize the total rate of D2D users under the condition that cellular users' rate requirements were met. Zhu et al. [11] proposed a channel allocation and power control algorithm for multiple D2D users and cellular users so as to make good use of uplink resources in cellular systems while ensuring the communication quality of common cellular users. Ban and Jung [12] proposed a centralized link access control algorithm to ensure maximum transmission rate for overlay D2D cellular users. However, D2D users occupied special spectrum resources and the spectrum utilization rate was not high, but this scheme was not suitable for underlay D2D communication. Qian et al. [13] proposed a joint channel selection and power control algorithm based on convex optimization to maximize the total rate of D2D users, without considering the access control problem of D2D users. A kind of interference-aware resource optimization for D2D communications in 5G networks was put forward by Hao et al. [14], but it did not take access control into account. e NP-hard joint resource allocation problem was formulated as a oneto-one matching problem, which also did not consider access control problem of D2D links [15]. A signal to interference plus noise ratio (SINR) aware mode selection, scheduling, and resource allocation scheme for D2D communications was put forward by Bithas et al. [16]. However, scheduling and resource allocation were considered individually. By exploiting D2D communication for enabling user collaboration and reducing the edge server's load, the D2D-assisted and nonorthogonal multiple access based mobile edge computing system was investigated by Diao et al. [17], which just considered power, channel allocation, and computing resources without taking D2D access control problem into account. e resource allocation problem for uplink multicarrier nonorthogonal multiple access in D2D underlay cellular networks was investigated by Zheng et al. [18], which did not consider D2D access control and energy minimization. A kind of power allocation scheme was put forward by Wang et al. [19] to maximize the energy efficiency of the relay-aided D2D link while satisfying the minimum data transmission rates of the cellular links, which did not consider the minimum data rate requirements of D2D links and the number of admitted D2D links.
Although some current works [6,7,16,20,21] considered access control and resource allocation, access control and resource allocation were optimized individually. Firstly, they determined whether a D2D pair can be admitted under the SINR requirements of both D2D users and cellular users. Secondly, they allocated resources to D2D users and cellular users to maximize the overall throughput or energy efficiency. In our research, access control and resource allocation were optimized jointly, not individually. While ensuring the minimum transmission rates of cellular links and D2D links, we not only minimize the power consumed by D2D users but also maximize the number of D2D users. Besides, each D2D link can reuse all subcarriers of cellular users. Specifically, the main contributions of this paper are listed as follows: (1) e optimization objective is to maximize the number of admitted D2D links and minimize the total power consumption of D2D links while meeting the minimum transmission rate requirements of D2D users and common cellular users. is optimization problem is transformed into a onestage problem. It is proved that joint access control and resource allocation can not only maximize the number of admitted D2D links but also minimize the total power consumption of D2D links. (2) In order to solve this problem, a continuous function is used to approximate binary discrete access control variable. e joint access control and resource allocation problem is transformed into a monotone optimization problem, which is worked out by reverse polyblock approximation algorithm. Besides, we prove that choosing appropriate parameters can maximize the number of admitted D2D links. In order to reduce computation complexity, a kind of iterative convex optimization algorithm is proposed. (3) Via numerical simulation, we demonstrate that the proposed algorithms can maximize the number of admitted D2D links and minimize the total power consumption of D2D links. e performance of two algorithms is better than that of the energy efficiency optimization algorithm.
is paper is organized as follows. In Section 2, we present the system model. e access control and energy minimization problem is transformed into a one-stage problem in Section 3. In Section 4, the solving algorithm of access control and energy minimization is put forward. Numerical results are presented in Section 5 followed by the conclusions in Section 6.

System Model
In the uplink transmission of a single-cell wireless cellular network as shown in Figure 1 , ∀n ∈ N represents power allocation vector of link m ∈ M on all subcarriers. We introduce a binary variable ρ n k for the cellular link k ∈ K. ρ n k � 1 represents that subcarrier n is assigned to link k; otherwise, ρ n k � 0. ρ � [ρ n ], ∀n ∈ N represents allocation vectors of all subcarriers; ρ n � [ρ n k ], ∀k ∈ K represents allocation vectors of all cellular links on subcarrier n.
Signal to interference plus noise ratio of cellular link k on subcarrier n is where l∈L p n l |h n kl | 2 represents interference from D2D link to cellular link k when reusing subcarrier n and σ n k represents noise power on subcarrier n of cellular link k. Signal to interference plus noise ratio of D2D link l on subcarrier n is where k∈K ρ n k p n k |h n lk | 2 represents interference from cellular link to D2D link l when reusing subcarrier n. l′∈L\l p n l′ |h n ll′ | 2 represents interference from other D2D links except for link l. σ n l represents noise power of D2D link l on subcarrier n. e spectrum efficiency of cellular link k ∈ K and D2D link l ∈ L is expressed, respectively, as

Access Control Problem and Energy Minimization
Problem. e first problem is access control of D2D links, which maximizes the number of admitted D2D links through subcarrier allocation, power allocation, and link access control while ensuring the transmission rates of cellular users and D2D users. A binary link access control vector s � [s 1 , s 2 , . . . , s L ] T is introduced to represent whether D2D link l meets the demand of minimum data rate. For any l ∈ L, s l � 0 means that the corresponding D2D link is scheduled; otherwise s l � 1. e optimization goal is to make as many as possible s l equal to 0, which means the sum of all elements in the vector s is as small as possible. e access control problem is formulated as P1: where R min k and R min l represent the minimum rate requirement of cellular user k ∈ K and D2D user l ∈ L, respectively, P max denotes the maximum power of each link, and ρ n k ∈ 0, 1 { } and k∈K ρ n k ≤ 1 mean that each subcarrier can only be assigned to one cellular link. Problem P1 can give the set of admitted D2D links L * � l | s * l � 0 . e second problem is to minimize total power consumption of the admitted D2D links L * � l | s * l � 0 , which can be expressed as P2: Complexity (12) and (15) ensure that each admitted D2D link meets the minimum transmission rate and maximum power requirement, respectively. (13) and (14) can ensure that each cellular link meets the minimum transmission rate and maximum power requirement, respectively.

One-Stage
Problem. Both P1 and P2 are NP problems [22,23], which makes us can no longer find their global optimum in polynomial time. We have to use a high quality approximation method to solve these two problems in polynomial time. erefore, effective suboptimal approximation is carried out to convert this two-stage problem into a one-stage problem P3: Proposition 1. By selecting appropriate α (α ≥ LP max ) and can not only maximize the number of admitted D2D links but also minimize the total power consumed by D2D links. e proof process is as follows.
Proof. Suppose that (ρ * , p * , s * ) is a feasible solution to problem P3, which satisfies constraint (18)- (24). e link vector s * that can be scheduled belongs to the set is also a feasible solution to problem P1. Similarly, suppose that (ρ ′ , p ′ , s ′ ) is a feasible solution to problem P1, which satisfies constraint (5)- (10), and the link vector s ′ that can be scheduled belongs to the set is also a feasible solution to problem P3. So, problem P1 and problem P3 have the same feasible set.
It is assumed that (ρ * , p * , s * ) is the optimal solution of problem P3, but it cannot maximize the number of admitted D2D links. However, there is another solution (ρ ′ , p ′ , s ′ ) that makes l∈L s * l ≥ l∈L s l ′ + 1, so that the following inequality is obtained: It can be seen from inequality (25) that the new feasible solution (ρ ′ , p ′ , s ′ ) can obtain smaller objective function value than the optimal solution, which is inconsistent with the fact that (ρ * , p * , s * ) is the optimal solution of problem P3, so problem P3 can maximize the number of admitted D2D links. e next step is to prove that P3 can minimize the power consumption of D2D links. Suppose that there is a feasible solution (ρ ′ , p ′ , s ′ ) which can maximize the number of admitted D2D links and can get lower D2D power consumption than (ρ * , p * , s * ) so that the following inequality can be obtained: Inequality (26) is inconsistent with the fact (ρ * , p * , s * ) is the optimal solution of P3, so P3 can maximize the number of admitted D2D links and minimize the power consumed by D2D links. Proposition 1 is proved completely.
In order to force cellular links to use orthogonal spectrum, the interference effects of other cellular links are considered, which is implemented by an introduced very large channel gain h v between cellular links [24] so that the signal to interference plus noise ratio of cellular link k on subcarrier n is reformulated as where k′∈K\k p n k′ h v represents interference from other cellular links on subcarrier n. Similarly, the signal to interference plus noise ratio of D2D link l on subcarrier n is e spectral efficiency of cellular link k ∈ K and D2D link l ∈ L is expressed, respectively, as So, problem P3 can be converted into P4: 4 Complexity Suppose that (ρ * , p * , s * ) is the optimal solution of P3, (p * , s * ) is a feasible solution of problem P4. If (p * , s * ) is an optimal solution of P4, the subcarrier allocation satisfies Each subcarrier is allocated to one cellular link at most, so (ρ * , p * , s * ) is an optimal solution of P3. erefore, the optimal solution of problem P4 is also the optimal solution of problem P3.
where Q is a small enough constant larger than 0, and this approximate function satisfies monotone increasing property, for s l � 0, q(s l ) � 0; for s l � 1, q(s l ) � 1. Problem P4 is converted into problem M1: Problem M1 is a nonconvex optimization problem, and the solving process is very complicated, but it has implied monotonicity. After appropriate transformation, this problem is transformed into a monotone optimization problem, which can be solved by reverse polyblock approximation method [25]. e regular monotone optimization has the following form: where f(x): R n + ⟶ R is a monotone increasing function, G ⊂ [0, b] ⊂ R n + is a nonempty normal set, and H is the inverse normal set belonging to [0, b].
If g(x): R n + ⟶ R and h(x): R n + ⟶ R are both increasing functions, G and H satisfying (42) are normal set and inverse normal set, respectively.
e objective function (38) is an increasing function. In order to transform M1 into a monotone optimization problem, all constraints in M1 need to be converted into the form of (42). R l (p) and R k (p) are nonincreasing functions of p. So, a new vector z� [z n m ] ∀m∈M,∀n∈N is defined. e variable z n m � c n m (p) represents the signal to interference plus noise ratio of the link m ∈ M on the channel n ∈ N. P � p | n∈N p n m ≤ P max , m ∈ M represents the maximum power constraint of the link m ∈ M, and x � (z, s) represents the optimization vector with dimension of D � L + (K + L)N. M1 is converted into the following form: is problem needs to minimize a monotone increasing function, G denotes the normal set which satisfies the constraints (48)-(50), and H denotes the reverse normal set which satisfies the constraints (44)-(47). e optimal solution of problem of M1 is located on the boundary of X � G ∩ H, so we can take advantage of the reverse polyblock approximation method to solve problem M1 as shown in Algorithm 1, where e d is a vector the elements of which are all zeros except that the d-th element is one and ⊙ represents the Hadamard product.
After Algorithm 1 is completed, binary access control vector s is obtained by carrying out rounding operation according to According to obtained z * , we can work out (p n m ) * using where (z n l ) (i) and (s l ) (i) , respectively, represent the values of z n l and s l in the i-th iteration. In order to determine whether ρ H (x (i) ) meets constraints (48)-(50), the solution of problem M1-1 is as follows: (58) So, (55) can be converted into For a given λ, M1-1 is transformed into the following linear programming problem: Initialization: e number of iterations is i � 1. Vertex set is V (1) � x (1) with x (1) � (z (1) , s (1) ) � 0 { }. Set CBV 0 � +∞.
Update the lower boundary f low � f(x (i) ).
(60) e above linear programming problem can be solved by the simplex method or interior point method.

Proposition 2.
In problem M1, s * l could be a fractional number, which is clearly not the optimal solution to problem P4. en, Algorithm 1 can maximize the number of admitted D2D links by choosing appropriate ε satisfying (

proof process is as follows.
Suppose that (z * , s * ) is the optimal solution of problem M1 and p * is the corresponding optimal power vector; if s * l is an integer, the proposition is proved. If s * l is a fractional number, suppose that s 0 and p 0 are the optimal access control vector and power allocation vector of problem P4, respectively.

Numerical Simulation
In order to test the performance of proposed algorithms, we perform numerical simulation based on MATLAB platform. In the wireless cellular network that supports D2D communication, the coverage radius of the base station is 500 m, the number of cellular links is K � 4, the number of D2D links is L � 26, and the number of subcarriers is N � 5. e maximum transmission power of the user is 23 dBm, the distance between D2D transmitting endpoint and receiving endpoint is randomly distributed between 10m and 50m, and the cellular users are evenly distributed in the cell. e numerical simulation parameters are shown in Table 1.
e minimum rate requirement of each cellular link is R min k � 2 bps/Hz, and the minimum rate requirement of each D2D link is R min l � 5 bps/Hz. All numerical results are obtained by averaging 1000 randomly implemented channel gains. In the numerical simulation process, reverse polyblock approximation algorithm is used to solve monotone optimization problem, low complexity algorithm represents the iterative convex optimization algorithm with low complexity, and maximizing energy efficiency algorithm represents the method which can maximize energy efficiency [27]. e energy efficiency is defined as the ratio of total sum rate to overall consumed power of all D2D links [27]. e comparison of access ratio of different algorithms is shown in Figure 2.
e reverse polyblock approximation algorithm has the highest access ratio, the access ratio of the iterative convex optimization algorithm with low complexity decreases about 5% on average compared with reverse polyblock approximation algorithm, and the maximizing energy efficiency algorithm has the lowest access ratio and is reduced by about 26% on average compared with reverse polyblock approximation algorithm.
e total power consumption comparison of different algorithms is shown in Figure 3. e power consumption of maximizing energy efficiency algorithm is greater than iterative convex optimization algorithm and reverse polyblock approximation algorithm. Iterative convex optimization algorithm consumes about 10% more power on average than reverse polyblock approximation algorithm. e power consumption of the maximizing energy efficiency algorithm is increased by about 30 times as much as that of reverse polyblock approximation algorithm. Figure 4 presents the objective function value of different algorithms. It can be seen from this figure that reverse polyblock approximation algorithm has the smallest objective function value, followed by the iterative convex optimization algorithm, and the maximum energy efficiency algorithm has the largest objective function value. e relationship between objective function value and D2D bit rate requirement is shown in Table 2. As the bit rate requirement of D2D links increases, the objective function value of reverse polyblock approximation algorithm increases from 15.1827 to 34.2001, the objective function value of iterative convex optimization algorithm increases from 22.9407 to 38.8148, and the objective function value of maximizing energy efficiency algorithm increases from 134.9136 to 192.5249. e average objective function value of maximizing energy efficiency algorithm is about 5 times that of iterative convex optimization algorithm on average. e objective function value of reverse polyblock approximation algorithm is reduced by about 20% on average compared with iterative convex optimization algorithm.
In order to test the access ratio and power consumption of D2D links under different number of cellular users, we perform another experiment. e number of cellular links is varied from 4 to 10, and the number of subcarriers is 10. e access ratio and power consumption under different number of cellular users are shown in Figures 5 and 6, respectively. As the number of cellular links increases, the access ratio of D2D links decreases and Step 1. Given link L 1 � L, initial power p (0) � 0 and iteration times i � 0.
Step 2. Repeat ALGORITHM 3: P4. 8 Complexity total power consumption increases. In this case, the interference from the cellular link increases, resulting in a decrease in the access ratio of the D2D link. In order to     meet transmission rate requirements of D2D links, more energy is required. It can be observed that reverse polyblock approximation algorithm and iterative convex optimization algorithm are superior to maximizing energy e ciency algorithm. e objective function value versus the number of cellular users is shown in Figure 7. Table 3 presents the numerical results, implying the relationship between objective function value and the number of cellular users. It is also validated that reverse polyblock approximation algorithm has the best performance, iterative convex optimization algorithm takes the second place, and maximizing energy e ciency algorithm has the worst performance.

Conclusions
In this paper, the problem of D2D link access control, subcarrier allocation, and power allocation in the uplink of single-cell D2D underlay cellular network is studied. e purpose is to maximize the number of admitted D2D links and reduce the power consumption of D2D links in the system while ensuring the minimum data transmission rate of cellular links and D2D links. It is di cult to solve the problem e ectively, so it is transformed into monotone optimization problem. en, reverse polyblock approximation algorithm is used to solve this monotone optimization problem. Because the monotone optimization problem has relatively high complexity, this paper proposes an algorithm based on iterative convex optimization with low complexity. e numerical results show that reverse polyblock approximation algorithm has the best performance, the low complexity algorithm based on iterative convex optimization has the suboptimal performance, and the algorithm based on energy e ciency maximization has the lowest access rate and the highest energy consumption.   Data Availability e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this article.